\chapter{General Insights}
\label{chap:insight}

In this chapter we will discuss random topics about the mental image
system.

\section{Correspondence with Sequence and Relationship}

The first thing we are going to look at is the correspondence between
sequence, relationship, the location of the designee, and the position
and nature of the allemande spot.

First it is worth repeating a statement made earlier:

\highlight{From lines facing in, lines facing out, 8-chain, trade by,
or waves {\em only\/}: If the designee is in front, his or her own sex
dancers are in sequence.  If in back, they are out of sequence.  If
the allemande spot is an \o, the men and women are in the same
sequence as each other (both in or both out).  If the spot is an \x,
they are in different sequence.}

While these statements are made in one direction they are also valid
reversed: boys in sequence means a male designee must be in the front
row, and boys and girls in difference sequence means the spot must be
an \x.

The only remaining piece to the puzzle is the location of the
allemande spot relative to the designee.  If we look at L1p lines:

\displayone
{ \gdancern 4s & \bdancern 4s & \gdancern 3s & \bdancern 3s \\
  \bdancern 1n & \gdancern 1n & \bdancern 2n & \gdancern 2n }
{}

\noindent we know from earlier that the designee can be the \#1 or \#3
boy, and in either case he is standing on his allemande spot (we could
call \call{allemande left}).  Let's choose \#1 as the designee:

\displayone
{ \gdancer s & \bdancer s & \gdancer s & \bdancer s \\
  \dbdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandeaO}

Now let's rotate the girls one position counter-clockwise:

\displayone
{ \gdancern 3s & \bdancern 4s & \gdancern 2s & \bdancern 3s \\
  \bdancern 1n & \gdancern 4n & \bdancern 2n & \gdancern 1n }
{}

We haven't changed the sequence, so the designee can still be the \#1
boy and the spot is still an \o.  But where is the allemande spot?  It
has moved one position to the right!  This is obvious if you consider
that you could call \call{slide thru, right and left thru, allemande
left} from here.  So the state is:

\displayone
{ \gdancer s & \bdancer s & \gdancer s & \bdancer s \\
  \dbdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandebO}

Further rotations of the girls with respect to the boys will simply
move the spot further to the right.  Also, although we won't work it
out in detail here, this spot motion is the same whether the spot is
an \o\ or an \x.

So, for those who are interested, here is a general method for reading
the mental image state from normal-sex lines.  This is not a method
designed to be used on the fly, but rather might be useful in writing
cards or experimenting.

\begin{enumerate}

\item If the boys are in sequence, the designee is the leftmost boy in
the front row.  If the boys are out of sequence, the designee is the
leftmost boy (from the caller's perspective) in the back row.

\item Look at the designee's partner.  Place the spot in the following
position: 1 plus the designee's couple number minus the designee's
partner's couple number.  Wrap around as usual if the spot number is
less than one.

\item If the boys and girls are in the same sequence, the spot is an
\o.  If they are in different sequence, the spot is an \x.

\end{enumerate}

Let's try an example:

\displayone
{ \gdancern 2s & \bdancern 3s & \gdancern 1s & \bdancern 4s \\
  \bdancern 2n & \gdancern 3n & \bdancern 1n & \gdancern 4n }
{}

The boys are out of sequence so the designee is here:

\displayone
{ \gdancer s & \dbdancer s & \gdancer s & \bdancer s \\
  \bdancer n & \gdancer n & \bdancer n & \gdancer n }
{}

The designee is \#3, and his partner is \#2, so we place the allemande
spot in position 2 ($1+3-2=2$).  The boys and girls are in a different
sequence, so the spot is an \x.  The final state is then:

\displayone
{ \gdancer s & \dbdancer s & \gdancer s & \bdancer s \\
  \bdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandebX}

For most people, it would be difficult to sight out of the original
setup without getting into a more familiar setup first.  A possible
getout might be:

\begin{sequence}
right and left thru \\
flutterwheel {\rm (at this point, many people would recognize an L2p
setup)} \\
slide thru \\
pass thru \\
allemande left
\end{sequence}

Let's look at resolving this same setup using mental image techniques
to see if we can't produce a more interesting resolve:

\begin{sequence}
slide thru \\
touch 1/4 (\x) \\
follow your neighbor and spread (\x) \\
girls trade (\x) \\
scoot back \\
right and left grand
\end{sequence}

or perhaps this one:

\begin{sequence}
spin the top (\x) \\
hinge (\x) \\
walk and dodge \\
chase right (\x) \\
hinge (\x) \\
left swing thru (\x) \\
step thru \\
allemande left
\end{sequence}

or if you're going for a quick getout:

\begin{sequence}
fan the top (\x) \\
step thru \\
allemande left
\end{sequence}

Notice how much flexibility the mental image system gives you over
canned sight resolves!

The above method of extracting state from a line can easily be
extended to other formations.  Rather than present separate methods
here, consider transforming your formation into a line, find the
state, and then ``untransform'' it back to your original setup
manipulating the state as appropriate.  For example, to find the state
of an 8-chain, simply have the dancers \call{slide thru}, find the
state, and then have them un-\call{slide thru}.

\section{Using Snapshot Resolves}

It is not necessary, or even necessarily desireable, to use the mental
image system exclusively during a sequence.  For example, you might
have memorized zeroes that are not easily handled within the mental
image framework, and you could easily insert them at various points in
a sequence.  Another possibility is to use full sight calling for the
main choreography, and mental image for the resolve.  Why would you
want to do this?  Most sight callers have their own method that they
use for resolving, and after a while it can get boring for the
dancers.  Consider the standard \call{ferris wheel, zoom, centers pass
thru} type of resolve.  It's easy to see, but can get old after a few
years.\footnote{There are some callers who believe that having a
predictable resolve is {\em good\/} --- it gives the dancers a chance
to relax and feel successful when they know the resolve is happening.
We'll leave it up to your judgment if you want to use predictable or
unpredictable resolves, or a mixture of the two.}  Instead, you could
find the mental image state for the square at a certain point, and
then use mental image calling to finish the resolve.  This gives you a
lot of flexibility and allows you to come up with unique resolves
every time.  But now we need a method for reading the mental image
state from a square.

There are two possibilities:

\begin{enumerate}
\item You can read the full state from any arbitrary setup (assuming
it's legal in the mental image system).  This can be complicated and
time-consuming to do on the fly, but might be possible.  We've given
the method in the previous section for normal-sex lines.

\item You can notice that you are in a state where you would perform
one of your normal resolves (like \call{star thru, pass thru,
allemande left}).  But instead of saying those calls, simply translate
it (by memory) into the corresponding mental image state.
\end{enumerate}

\noindent It is this second method that we will look at here.

Research performed by Bill Davis and Kip Garvey \cite{something} has
shown that the vast majority of sight callers see partner pairing as
the first stage in sight resolution.  Out of the 16 possible
normal-sex lines, there are only six that have at least one couple
paired with original partner.  These six lines are shown below along
with their mental image equivalent.  Any sight caller who is able to
snapshot one or more of these setups will be able to instantly know
the mental image state, and thus could use the mental image system to
resolve from then on.  Most sight callers can probably identify the
L1p and L2p setups, and the others can be recognized with practice.

\displaytwo
{ \gdancern 4s & \bdancern 4s & \gdancern 3s & \bdancern 3s \\
  \bdancern 1n & \gdancern 1n & \bdancern 2n & \gdancern 2n }
{L1p: Everyone paired, corners adjacent}
{ \gdancer s & \bdancer s & \gdancer s & \bdancer s \\
  \dbdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandeaO}

\displaytwo
{ \gdancern 2s & \bdancern 2s & \gdancern 3s & \bdancern 3s \\
  \bdancern 1n & \gdancern 1n & \bdancern 4n & \gdancern 4n }
{L2p: Everyone paired, corners not adjacent}
{ \gdancer s & \dbdancer s & \gdancer s & \bdancer s \\
  \bdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandeaO}

\displaytwo
{ \gdancern 4s & \bdancern 2s & \gdancern 3s & \bdancern 3s \\
  \bdancern 1n & \gdancern 1n & \bdancern 4n & \gdancern 2n }
{L4p: Left end paired, all facing corner}
{ \gdancer s & \dbdancer s & \gdancer s & \bdancer s \\
  \bdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandecX}

\displaytwo
{ \gdancern 4s & \bdancern 4s & \gdancern 1s & \bdancern 3s \\
  \bdancern 1n & \gdancern 3n & \bdancern 2n & \gdancern 2n }
{L3o: Right end paired, all facing corner}
{ \gdancer s & \bdancer s & \gdancer s & \bdancer s \\
  \dbdancer n & \gdancer n & \bdancer n & \bdancer n }
{\allemandecX}

\displaytwo
{ \gdancern 2s & \bdancern 4s & \gdancern 3s & \bdancern 3s \\
  \bdancern 1n & \gdancern 1n & \bdancern 2n & \gdancern 4n }
{L3p: Left end paired, none facing corner}
{ \gdancer s & \bdancer s & \gdancer s & \bdancer s \\
  \dbdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandeaX}

\displaytwo
{ \gdancern 4s & \bdancern 4s & \gdancern 3s & \bdancern 1s \\
  \bdancern 3n & \gdancern 1n & \bdancern 2n & \gdancern 2n }
{L4o: Right end paired, none facing corner}
{ \gdancer s & \dbdancer s & \gdancer s & \bdancer s \\
  \bdancer n & \gdancer n & \bdancer n & \gdancer n }
{\allemandecX}

Similar to the six lines shown above are six 8-chain setups that have
at least one couple paired.  By far the most commonly recognized is
B1c, although is B4c is also common.  The other four can also be
learned with practice.  It is interesting to note that these setups
are simply the six presented above with each box rotated 90 degrees
clockwise.

\displaytwo
{ \bdancern 1e & \gdancern 4w & \bdancern 2e & \gdancern 3w \\
  \gdancern 1e & \bdancern 4w & \gdancern 2e & \bdancern 3w }
{B4c: All paired, outside man facing corner}
{ \dbdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \bdancer w & \gdancer e & \bdancer w }
{\allemandebX}

\displaytwo
{ \bdancern 1e & \gdancern 2w & \bdancern 4e & \gdancern 3w \\
  \gdancern 1e & \bdancern 2w & \gdancern 4e & \bdancern 3w }
{B3r: All paired, outside man not facing corner}
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w & \gdancer e & \bdancer w }
{\allemandebX}

\displaytwo
{ \bdancern 1e & \gdancern 4w & \bdancern 4e & \gdancern 3w \\
  \gdancern 1e & \bdancern 2w & \gdancern 2e & \bdancern 3w }
{B1c: Outside paired, all facing corner}
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w & \gdancer e & \bdancer w }
{\allemandebO}

\displaytwo
{ \bdancern 2e & \gdancern 1w & \bdancern 3e & \gdancern 2w \\
  \gdancern 4e & \bdancern 1w & \gdancern 3e & \bdancern 4w }
{B2c: Inside paired, all facing corner}
{ \dbdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \bdancer w & \gdancer e & \bdancer w }
{\allemandebO}

\displaytwo
{ \bdancern 1e & \gdancern 2w & \bdancern 2e & \gdancern 3w \\
  \gdancern 1e & \bdancern 4w & \gdancern 4e & \bdancern 3w }
{B2r: Outside paired, not facing corner}
{ \dbdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \bdancer w & \gdancer e & \bdancer w }
{\allemandedO}

\displaytwo
{ \bdancern 4e & \gdancern 1w & \bdancern 3e & \gdancern 4w \\
  \gdancern 2e & \bdancern 1w & \gdancern 3e & \bdancern 2w }
{B1r: Inside paired, not facing corner}
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w & \gdancer e & \bdancer w }
{\allemandedO}

\section{Other Stuff}

We can also make the following observation:

\highlight{If the allemande spot is an \o\ in location 1 or 3 (or an
\x\ in location 2 or 4) then there are an {\em even\/} number of key
dancers in each box.  If the allemande spot is an \o\ in location 2 or
4 (or an \x\ in location 1 or 3) then there are an {\em odd\/} number
of key dancers in each box.}

In more traditional calling terminology, an even number of key dancers
implies some sort of ``line'' getout, such as \call{star thru, square
thru 3, allemande left}.  An odd number of key dancers implies some
sort of ``box'' getout such as \call{pass to the center, centers
square thru 3, allemande left}.  The even/odd nature of the setup can
be changed by exchanging two dancers across the set, for example with
an \call{acey deucey}.